Showcasing the use of Factor Analysis in data reduction: Research on learner support for In-service teachers Richard Ouma University of York SPSS Users Conference (ASSESS), Alcuin Research Resource Centre Auditorium, University of York, York 10th November, 2017

Introduction of the study The research explored learners’ perceived quality of support from the university and addressed the question: What perceptions do distance education in-service teachers have about the quality of learner support delivered to them? A 45 item questionnaire was used to measure various aspects of learners’ perceived quality of support. Each question was a statement followed by a five-point Likert scale ranging from strongly disagree to strongly agree. Factor analysis involving principal components analysis (PCA) with oblique rotation (direct oblimin) using SPSS Version 23 was used in the analysis.

Meaning of Factor Analysis “Factor analysis is a mathematical procedure which reduces a correlation matrix containing many variables into a smaller number of factors or supervariables” (Howitt & Cramer, 1997 p.287). Why factor analysis in this investigation? The purpose was to explore the possibility of reducing a large set of 45 variables on learner support to fewer manageable and representative factors (factor analysis discovers latent factors from a variety of related variables).

Suitability of the data for Factor Analysis Normality was tested using normality plots with tests and histogram, and normal probability plots (Normal Q-Q Plots)- the scores showed reasonably normal distribution. The SPSS statistical output revealed straight-line relationships between the variables (linear relationships). Multicollinearity was not detected (the determinant of the R-matrix was .0008676 which is > .00001 KMO was .865 (great as per Field, 2009), and is > the recommended minimum value of .6 Kaiser 1970, 1974). The Bartlett’s Test of Sphericity was statistically significant with p = .000 hence p < .05 (Bartlett, 1954). Content of the factor correlation matrix revealed many high factor loadings above .3

Data reduction – Kaiser's Criterion Initial Eigenvalues Factor Total % of variance Cumulative % 1 10.081 22.401 22.401 2 2.650 5.889 28.291 3 2.289 5.087 33.378 4 1.886 4.191 37.569 5 1.505 3.345 40.915 6 1.451 3.225 44.139 7 1.386 3.081 47.220 8 1.287 2.861 50.081 9 1.177 2.616 52.696 10 1.093 2.430 55.126 11 1.062 2.360 57.486 12 1.035 2.300 59.786 13 1.004 2.231 62.017

Data reduction – Carttel’s Plot

Total Variance Explained of Four Extracted Factors Initial Eigenvalues Factor Total % of variance Cumulative % 1 10.081 22.401 22.401 2 2.650 5.889 28.291 3 2.289 5.087 33.378 4 1.886 4.191 37.569

Internal measure of consistency Factor Question number Cronbach’s Alpha (α) Academic advising support 23,43,41,42,21,3,22,1,28,32,9,34,27,24,33,35,11,26 .854 Library and technology support 15,31,30,13,10,16,20,14,8 .831 Counselling and career support 37,38,36,40,25,44,39,17,29 .803 Communication service support 5,12,6,7,45,4,2,18, 19 .704 All constructs produced a significant reliability with Cronbach’s alpha > .7, which should be the minimum for a factor to be retained for further analysis and decision making based on the rule of the thumb (Field, 2009).

Concluding remark Using factor analysis statistical technique, the 45 initial variables were reduced to 4 factors showing learners’ perceived quality of support from the university. These 4 factors generated quantitatively were later explored in the field using qualitative methods. Thank you for your active Listening.